Membrane-Supported Liquid-Liquid Extraction – Where Do We Stand Today? Wolfgang Riedl[1],* Abstract Thanks to advances in materials science and manu- task as well as to optimize the module design. Rapid facturing technology, membranes are now available tests can determine the basic suitability and kinetic for stable liquid-liquid extraction processes. Rigor- parameters. Thus, the general requirements for ous calculation models can be used to calculate the exploiting the specific advantages of this separation membrane areas required for a specific separation technology in technical applications are fulfilled. Keywords: Mass transfer model, Membrane-assisted liquid-liquid extraction, Membrane contactors Received: October 25, 2020; accepted: January 13, 2021 DOI: 10.1002/cben.202000032 This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. 1 Introduction the second half of the last century. The materials investigated included Polypropylene (PP), Polyvinylidene Fluoride (PVDF), Membrane contactors occupy a special position within mem- Polytetraflourethylene (PTFE), and Polysulfone (PSU). Inor- brane processes: instead of filtering, they passively separate two ganic materials (ceramics) were not used initially. fluid phases by acting as artificial interfaces. Of the two phases The first technically available membrane contactors were involved, usually only one wets the membrane, while the other produced from tubular PP membranes (3M/LiquiCel). Manu- phase is retained. Together with the characteristic membrane factured as hollow fibres (with diameter < 300mm) and packed properties, this results in a wide range of possible separation as bundles, such devices provide high volume-specific exchange 2 –3 technology applications. The specific properties of membrane surfaces of up to 30 000m m [7]. The compact design and contactors will be demonstrated using liquid-liquid extraction good availability of these membrane contactors elevated this as an example. technology to obtain first references [8] and thus increased awareness. However, the chemical and thermal stability of these membranes is limited by the materials used and especially 2 Development History by the challenge of cross-contamination-free cleaning of the densely packed hollow fiber bundles [9]. At the beginning of Membrane-supported liquid-liquid extraction was first this millennium, the first membranes were manufactured from described in depth in 1984 by Kiani et al. [1]. Since then, this inorganic materials [10] and tested for use under demanding technique has been described in detail time and again, e.g., in conditions [11]. Today, however, due to new joining and fasten- the review articles by Gabelman and Hwang [2], Pabby and ing techniques possible with 3D printing, membrane contac- Sastre [3], a special issue of the Journal of Membrane Science tors with tubular PTFE membranes have recently become [4] and inclusion in the monographs of Baker [5], Cussler [6], available [12]. Thus, membrane contactors and not just sole and Melin and Rautenbach [7]. membranes can be tested and piloted under demanding boun- The development history of potential membrane contactor dary conditions (e.g., metal salt extraction at very low pH val- applications has always been directly related to the availability ue) or hygienic applications (food, pharmaceuticals, consumer of membranes and their shape. Thus, developments in materi- health) requiring high temperatures for cleaning-in-place. als science were and are a strong driver for spreading this tech- nology. As a typical mass transfer device, the preferred mem- brane shape for membrane contactors is tubular. However, ————— membrane tubes are in general less suitable for research pur- [1] Prof. Dr.-Ing. Wolfgang Riedl poses, as connecting them to lab equipment and sealing them School of Life Sciences FHNW, Hofackerstrasse 30, 4132 Muttenz, is more demanding than with flat-sheet membranes. Therefore, Switzerland. the first investigations were mostly carried out with flat-sheet Email: wolfgang.riedl@fhnw.ch membranes, which have been available in various forms since {English version of DOI: https://doi.org/10.1002/cite.201900070 www.ChemBioEngRev.de ª 2021 The Authors. ChemBioEng Reviews published by Wiley-VCH GmbH ChemBioEng Rev 2021, 8, No. 1, 6–14 6 3 Operating Principle – Large volume-specific exchange surfaces, especially when using capillary and hollow fiber modules (up to 2 –3 In principle, all porous membranes with pore sizes well below 30 000 m m ). 1mm can be used in membrane contactors. Thus, both ultra- – As long as the wetting properties of the two phases are and (fine) microfiltration membranes can be applied. In this clearly different, liquid-liquid extraction is also possible with case, however, the membranes do not ‘filter’, but serve as an systems forming a homogeneous liquid phase under these artificial interface between two fluid phases, of which only one conditions, instead of two immiscible phases. needs to be a liquid. Ideally, one of the two phases wets the There is thus a fairly broad field of applications for mem- membrane and enters the membrane pores (due to capillary brane contactors in liquid-liquid extraction, as shown in Fig. 2. forces), while the second phase does not wet the membrane (Fig. 1). NTU As Fig. 1 shows, the phase interface between the two liquids forms at the pore exits of the membrane on the side where the non-membrane wetting liquid phase is located.To prevent the rotang / wetting phase from entering the non-wetting phase, the latter pulsed columns can be put under a certain overpressure. Normally, overpres- mixer seler sure lower than 400mbar is sufficient for this purpose [7]. This transmembrane pressure ensures that the phase interface is immobilized even during start-up and shut-down processes at the pore exit. It is important to note that the process is not a centrifugal extractors pressure-driven membrane process, but is based on the diffu- sion of the component(s) passing from one fluid phase into packed another, driven by a difference in chemical potential. columns For liquid-liquid extraction purposes, the immobilization of density difference the phase interface at the membrane pores offers the following advantages/benefits: Figure 2. Operational field of membrane-supported liquid-liq- – No energy input necessary to disperse one phase in the uid extraction in comparison to conventional extraction appara- other. tus (based on [13]). – No phase separation required after extraction. – The risk of stable emulsions forming is largely limited. As Fig. 2 shows, membrane contactors generally have no – No density difference between the liquid phases necessary restrictions with regard to the density difference and the num- (as no phase separation is required). ber of theoretical steps NTU. Of particular interest, however, – Phase ratios can be freely selected in wide ranges. are applications where low density differences occur and thus – Temperatures can be different in the individual phases. the phase separation in conventional liquid-liquid extraction can only be achieved by an applied centrifugal force. This is not necessary when membrane extraction is used. As long as there are no restrictions on the mem- brane materials used (e.g., chemical p resistance, no extractable constituents, good cleanability, etc.), the advantages of the membrane-supported liquid- liquid extraction are obvious and are therefore already at an advanced stage Membrane of development [13–21]. Multi-stage processes are also possible and have already been described [22].The mem- brane itself, however, generates an Transioning additional mass transfer resistance component Phase boundary missing from conventional liquid- liquid extraction. Studies have shown that this resistance can amount to up Liquid phase 1 Liquid phase 2 to 40% of the total resistance in mem- (weng) (non-weng) brane-assisted liquid-liquid extraction [23]. It is therefore desirable to keep the membrane thickness and hence the corresponding mass transfer re- sistance as small as possible. This is, however, difficult to reconcile with the Figure 1. Basic principle of membrane-supported liquid-liquid extraction. requirements for stable operation and www.ChemBioEngRev.de ª 2021 The Authors. ChemBioEng Reviews published by Wiley-VCH GmbH ChemBioEng Rev 2021, 8, No. 1, 6–14 7 solid membrane contactor construction and design. Thin- dMem walled polymer hollow fiber or capillary membranes (with wall 1 2 thickness < 150m) therefore have an advantage in this respect c over ceramic capillary membranes (with up to 3000m wall Co, thickness) for instance. Cog Finding the optimal membrane geometry is therefore a typi- cal engineering optimization and manufacturing problem, which must also be seen in the context of the advantages of tansferredcomponent membrane-supported liquid-liquid extraction (e.g., no phase Cogg solvent 1 separation after extraction). Therefore, the development of solvent 2 new, specially manufactured membrane geometries may be Cwgg beneficial. In order to reduce the number of samples required Cw, for this purpose, it is especially useful to predict the most favor- able wall thickness by using rigorous mass transfer models. y Figure 3. Concentration profile during extraction from the or- 4 Mass Transport Modelling ganic donor phase with water using a hydrophobic microporousmembrane. Mass transport for the component to be extracted in mem- brane-supported liquid-liquid extraction can be described us- quantity of the extraction of the main component. However, if ing the classical Lewis two-film model, extended by the addi- the mutual solubility of the solvents is low, this influence is tional transfer step of diffusion through the membrane pores negligible. [24]. It is assumed that a laminar film is formed at the phase According to the mass transport model shown in Fig. 3, the boundaries between liquid and membrane on both sides of the individual transport steps can now be described quantitatively membrane. At the interface the two liquid phases are in equi- using the assumptions made. Following the general form of the librium. Mass transfer perpendicular to the direction of flow of description of mass transport the two liquid phases takes place by molecular diffusion. The driving force for the mass transfer is the difference Dm dni ¼ n_ ¼ KoAðco  NcwÞ (3) in the chemical potentials of the transferring component i in dt the two liquid phases:     with n = molar amount of transferred component, K = overallmass transfer coefficient, A = mass transfer area, N = Nernst Dm ¼ ma  mbi i i ¼ RT lnaa  lna b i i þ Vi pa  pb (1) distribution number, and c1, c2 = molar concentration in liquid 1 and 2, the mass transfer from the dispensing organic phase With mi = chemical potential, R = universal gas constant, through the laminar boundary layer d1 can be described as: T = temperature, ai = activity of component i, Vi = partial   molar volume of (dissolved) component i, p = transmembrane n_ 1 ¼ koA0 co  cog (4) pressure, and a, b = fluid phase index. Prasad et al. [25] have shown that the second summand in with ko = mass transfer resistance for the transport through the Eq. (1) is small compared to the first term at the previous small organic boundary layer and Ao = organic boundary layer area. pressure differences between the two liquid phases and can The mass transfer through the membrane filled with organic therefore be neglected. It is further assumed that the activity ai solvent (hydrophobic membrane) can be expressed with: can be expressed by a concentration ci. The driving force in the   membrane-supported liquid-liquid extraction can then be n_ 2 ¼ kMemAMem cog  cogg (5) expressed approximately by the difference in the concentra- tions of a dedicated component passing through the two liquid whereas kMem = membrane mass transfer resistance and phases, taking into account the distribution number Vz AMem = membrane area. (derived from the Nernst distribution number N for highly di- The mass transfer through the aqueous laminar boundary luted solutions): layer d2 is described as following:   cogg n_ 3 ¼ kwAw cwgg  cw (6) Vz ¼ (2) cwgg whereas kw = aqueous boundar layer mass transfer resistance Fig. 3 shows the concentration profile during the extraction and Aw = aqueous boundary layer area. of a component from the organic phase into an aqueous re- For all three transfer steps, the molar rate must be equal: ceiver using a hydrophobic membrane. This mass transfer model takes into account the fact that in addition to the transi- n_ 1 ¼ n_ 2 ¼ n_ 3 ¼ n_ (7) tion component, both solvents are also extracted up to their maximum mutual solubility. These co-extractions influence the The mass transfer resistances ko, kMem, and kw are defined as following: www.ChemBioEngRev.de ª 2021 The Authors. ChemBioEng Reviews published by Wiley-VCH GmbH ChemBioEng Rev 2021, 8, No. 1, 6–14 8 Do been shown to be (currently) the minimum possible in termsko ¼ (8)d1 of mechanical strength and the feasiblity of installation in membrane contactors.With Eq. (7) and the assumption that all with D0 = diffusion coefficient of transferred component in surfaces are equally large, follows: organic phase and d1 = boundary layer thickness. A ” Ao ¼ AMem ¼ Aw (11) D k o e Mem ¼ (9)dMem t Taking Eqs. (2) and (8)–(10) into consideration, Eq. (3) can be expressed as follows: with e = porosity, t = tortuosity, and dMEM = membrane thick- ness. k k k 3n_ ¼ o Mem w A ðc  Vzc Þ ¼ 0 kMemkw þ1kokw þ kMemkoVz A2 o w kw ¼ Dw (10) d 12 @ A (12) 1 þ 1 Vz Aðco  VzcwÞ þ k k k With Dw = diffusion coefficient of transferred component in o Mem w aqueous phase. The sum of mass transfer coefficient (first bracket term in The diffusion coefficient Do for diffusion through the organic Eq. (12)) can then be combined to the over-all mass transfer boundary layer and through the hydrophobic membrane wet- coefficient Ko: ted by the organic solvent are assumed to be equal. In order to make the mass transfer step through the mem- 0 1 brane (Eq. (3)) as large as possible, the membrane mass transfer Ko ¼ @ 1 A coefficient k (Eq. (9)) must also become as large as possible. 1 þ 1 þ Vz (13) Mem k k k This can be realized if the membrane has a very low thickness o Mem w and/or a very low tortuosity, while at the same time having the With this and with the volume-specific exchange area a of highest possible pore ratio. Here, the membrane manufacturers the corresponding membrane contactor, the desired depletion are then required to generate a membrane that is optimal rate, the distribution number of the transferring components under these conditions and also meets the requirements for sta- in the two liquid phases and the velocity in the organic phase, ble operation. Fig. 4 shows a SEM image of a PTFE membrane. the contactor length or number of membrane contactors of a given length in series required for this separation task can be calculated: Zc1w ¼ v1 dcL 1 ¼ HTU  NTU (14)Ka c1 Vzc2 c1a with v1= velocity of the organic discharge phase, c1 = Concen- tration of the transferred components in the discharge phase and c2 = Concentration of the transferred components in the extraction phase, and a, w = indices for concentration at entry into (a) and exit from (w) the apparatus. 5 Experiments In general, models for describing mass transfer must first be provided with reliable data at central points in order to deliver reliable results: while the membrane characterization is usually reported by the manufacturers themselves as a production-tech- nical quality feature, or, as shown above (Fig. 4), can be made accessible via (complex) imaging techniques, the diffusion coef- Figure 4. SEM image of a tubular PTFE membrane (front view ficient of a transferring component in a liquid and at a given of ion-cut wall thickness). temperature is, for example, often unknown. Thus, experiments are inevitable.A suitable experimental setup for such a purpose is shown in Fig. 5. To carry out the experiments, first a mem- Fig. 4 clearly shows how the surface of the membrane has a brane module with a known surface area and (membrane) ge- high proportion of pores, but in the substructure of the mem- ometry is installed. Then, the desired quantities of feed and sol- brane the channels branch out quickly (high tortuosity). The vent phase are placed in the two vessels and tempered if wall thickness of the membrane is about 200mm, which had required. Figs. 6 and 7 show the test setup and membrane www.ChemBioEngRev.de ª 2021 The Authors. ChemBioEng Reviews published by Wiley-VCH GmbH ChemBioEng Rev 2021, 8, No. 1, 6–14 9 modules used as examples for corresponding tests (tubular PTFE membranes, MemO3 GmbH). It is benefical to start by pumping the phase that does not wet the membrane while the other phase is not yet pumped. Then, while continuing pump- ing, this phase is carefully placed under a certain overpressure (e.g., 100mbar). If no phase break- through into the second (still empty) side of the membrane (module) can be detected after a few minutes, pumping of the second phase can be started there as well. Thus, the membrane-sup- ported fluid-fluid contact is started (t0). In co-current operation mode, a typical curve is obtained for the concentration of the transferring component depending on the fluid dynamic parameters, the membrane selected and its character- istics (transfer area, material, wall thickness, porosity, tortuosity, swelling behavior) and the temperature: Figure 5. Scheme of experimental setup for membrane-supported liquid-liquid The concentration in the feed phase shows the course extractions experiments. of a decay function and in the solvent phase that of a saturation function, as shown in Fig. 8. The starting value for the concentration in the discharge phase is the weight of the passing component, for the extrac- tion phase it is that of the initial load (usually, however, zero). The corresponding final values can be easily determined, e.g., by a shaking test under identical conditions (if necessary with phase separation by centrifugation) and are also achieved with membrane-supported liquid-liquid extraction (after sufficient time), as the membrane does not influence the final equili- brium value. If the specific mass flow dn/(dt A) is plotted against the driv- ing force, the overall mass transfer coefficient K can be deter- mined from the gradient of the resulting line of origin [26]. With this experimental procedure, with a manageable amount of apparatus and time, it can be shown that this tech- nique can also be used to extract systems that tend to form Figure 6. Test setup according to scheme of experimental set- emulsions without the formation of emulsions (clear extracts, up (Fig. 5). clear raffinates) and thus the principle feasibility is given. If no emulsion formation occurs, the overall mass transfer coefficient K of this membrane-supported liquid-liquid extraction process can be determined by continuing the test for a sufficient time (and recording the concentration curves - see above) according to Eq. (12). Thus, the central parameter in Eq. (14) is available and process design can be carried out based on a rigorous mass transfer model with dedicated substance data. Using the example of the extraction of e-caprolactam from toluene into an aqueous phase, this approach resulted in the to- tal mass transfer coefficients K shown in Fig. 9 for different (flat) sheet membranes. As Fig. 9 shows, different K values are obtained with different membranes. This can be explained on the one hand by different wall thicknesses of the membrane samples and the longer diffusion paths associated with them. On the other hand, the porosity of the membranes also has a significant influence on the overall mass transfer coefficient K: the area entering Eq. (3) is generally to be understood as the area available for mass transfer - which in this case is the area resulting from all membrane pores. As a technically accessible surface, however, it is rather unsuitable, since only the installed Figure 7. Membrane modules used. surface, i.e., the total geometrical surface, is used for experi- www.ChemBioEngRev.de ª 2021 The Authors. ChemBioEng Reviews published by Wiley-VCH GmbH ChemBioEng Rev 2021, 8, No. 1, 6–14 10 ments (for flat sheet membranes the cut- to-size total surface or for capillary and hollow fiber membranes the surface result- ing from the tube geometry and length). For the same installed area, it is therefore not surprising that a membrane with a higher porosity (= higher proportion of pores, e.g, ‘PTFE membrane 1’ with e = 75%) also has higher overall mass transfer coefficients than, e.g., ‘PP mem- brane 1’ (e = 37). For the sake of completeness it should be mentioned that with the commonly used tubular membrane geometries (hollow fibers or capillaries with max. outside diameters < 3mm) it is not necessary to differentiate whether the exchange surface is located more at the inner or outer pore Figure 8. Temporal course of the concentration of caprolactam during membrane-sup- radius outlet (and thus the inner or outer ported extraction in a co-current operation mode. Direction of mass transfer organic to tubular radius must be used for calculation aqueous, circulation test in co-current mode, phase ratio 1:1, flow rates in both circuits = accordingly), as the wall thicknesses are 200mLmin–1, 25 C extraction temperature, concentrations determined by GC analysis usually small compared to the installed (multiple determination; +5% accuracy). total surface. In addition to the influence of the mem- brane (geometry) used on the overall mass transfer coefficient, further experiments confirmed that the 1,00E-04 membrane-supported extraction process, as can be derived from Eqs. (8)–(10), is also dependent on the selected tempera- 8,00E-05 ture and fluid dynamics [1, 3, 23, 26]. The influence of temperature on the overall mass transfer 6,00E-05 coefficient is expressed here above all by the dependence of the 4,00E-05 diffusion coefficient of the passing components on tempera- ture; it increases with increasing temperature. At the same 2,00E-05 time, however, solubility is also influenced, which according to Eq. (3) is also expressed in an altering driving force term. 0,00E+00 However, this fact can then also be used to determine the usu- ally rather less available diffusion coefficient D of a target com- ponent in a solvent at a selected temperature from tests with a well-characterized membrane (cf. Fig. 4) via the overall mass transfer coefficient K obtained from membrane-supported Figure 9. Experimental overall mass transfer coefficients for extraction tests [28].As expected, the influence of the fluid membrane-assisted liquid-liquid extraction of e-caprolactam, dynamics is shown by the boundary layer resistances forming Direction of mass transfer from organic phase to aqueous on both sides of the membrane: with increasing flow velocity; phase, co-current operation, phase ratio 1:1, flow rate in both these become smaller and thus the total mass transfer coeffi- loops = 200mLmin–1, 25 C extraction temperature. cient obtained becomes larger. It could be shown that a signifi- cant increase can be observed here, especially in the range of Table 1. Properties of the membrane used for the investiga- Reynolds numbers up to 300. Above this, the K value increases tions. only slightly with an increasing Reynolds number [23]. With the dependencies of the overall mass transfer coefficient Membrane Thickness Porosity e Tortuosity t K determined in this way, further experiments based on equa- [mm] [%] [–] tion 12 can be reliably predicted. Meanwhile, predictions which agree well with the data experimentally determined later under PTFE-Membrane 1 ca. 50 75 1.2–1.8 these conditions are successful with scale-up factors of more PTFE-Membrane 2 ca. 50 75 1.2–1.8 than 100 – for co-current and counter-current operation [29]. An experiment underlining the basic principles of this PTFE-Membrane 3 ca. 50 75 1.2–1.8 membrane process based on wetting/non-wetting of the mem- PP-Membrane 1 ca. 25 37 2.6–3.0 brane [23] is described below: Here the concentration of the PP-Membrane 2 ca. 100 65 ca. 3 component to be extracted -e-caprolactam- in the aqueous do- nor phase and the feed phase (toluene) was adjusted differently www.ChemBioEngRev.de ª 2021 The Authors. ChemBioEng Reviews published by Wiley-VCH GmbH ChemBioEng Rev 2021, 8, No. 1, 6–14 11 Over-all mass transfer coeffcient m/s and the capillary rise height of the respective solution in a poly- from the phase diagram, a mixture of two solutions (1 and 5 propylene hollow fibre was measured. The obtained results are from Tab. 2) in a ratio of 6.6:1 would result in a corresponding shown in Tab. 2. mixing point in the homogeneous liquid phase region. A con- ventional liquid-liquid extraction would no longer be possible Table 2. Solution mixtures and their capillary rise heights under these boundary conditions. (dK = 230mm). However, since solution 5 (toluene/e-caprolactam) completely wets the membrane used and solution 1 (water) does not wet the Test solution Concentration membrane, a membrane-supported liquid-liquid extraction is at (20 C) Caprolactame Water Toluene Capillary rise least theoretically possible under these conditions. [wt%] [wt%] [wt%] height [mm] A membrane-supported liquid-liquid extraction carried out with these solutions in the chosen ratio yielded the following re- 1 (pure 0 100 0 0.0 solvent) sult (Fig. 11). As shown in Fig. 11, it was possible to extract capro- lactam from the organic phase to the aqueous phase over a longer 2 20 80 0 0.0 period of time. This resulted in concentrations of over 40wt% in 3 61 29 10 19.0 the aqueous phase. It was only through the co-extraction of the solvent, which, according to the phase diagram, is distributed in 4 60 20 20 31.1 both liquid phases under the selected boundary conditions, that 4’ 83 17 0 0.0 wetting of the aqueous phase also increased after about 5 h and finally led to a phase breakthrough (= end of the test). 5 (Feed) 70 5 25 34.5 Until then, however, it was possible to extract from the 6 60 18 22 33.0 donor phase into the receiver phase without any problems. This is not possible with any other conventional liquid-liquid 7 25 0 75 47.5 extraction technology and could thus be a promising approach, 8 0 0 100 48.0 e.g., for yield improvement through side stream extraction. As Tab. 2 shows, the capillary rise height increases with 6 Summary and Outlook increasing toluene content. At a toluene content of 10% by weight (solution 3), the solution in the hollow PP fiber already Membrane-supported liquid-liquid extraction or membrane- reaches a rise height of 19mm. At a toluene content of 20% by supported fluid-fluid contact in general represents an interest- weight, the measured rise height was 31.3mm, which is hardly ing, innovative separation process with a high degree of different from the measured rise height of the feed solution robustness. Objections to the use of this technology, which (solution 5) of 34.5mm. were previously based on chemical stability or special require- At 20 C the ternary phase diagram, shown in Fig. 10, results ments for hygienic design (cleanability), can now only be for the above-mentioned substance system. As can be seen upheld to a limited extent, particularly through the use of PTFE Caprolactam Heterogeneous solid-liquid Heterogeneous liquid-liquid Homogeneous liquid Water Toluene Figure 10. Sample composition; shown in the triangular diagram of the substance system water/caprolactame/toluene (20 C). www.ChemBioEngRev.de ª 2021 The Authors. ChemBioEng Reviews published by Wiley-VCH GmbH ChemBioEng Rev 2021, 8, No. 1, 6–14 12 Figure 11. Concentration curve for caprolactam in water at extraction with mixing point outside the heterogeneous liquid-liquid region, direction of mass transfer organic to aqueous, co-current opera- tion, phase ratio 6.6:1, volume flow in both circuits = 200mLmin–1, 25 C extraction temperature, donor concentration: 70wt%, water phase initially un- loaded, PP Membrane 1. membranes. With a well-designed experimental setup, it is pos- Symbols used sible to generate mass transfer information in a short time with limited equipment requirements. Together with the availability A [m2] (mass) transfer area of membrane contactors in various (standard) designs and a [m2m–3] specific transfer area technology that can be easily scaled-up using rigorous mass a [–] activity transfer models, a foundation has been laid for applying and D [m2s–1] diffusion coefficient extending the specific advantages of membrane-supported flu- HTU [m] height of a transfer unit id-fluid contact to new areas of application. Therefore, it does K [m s–1] overall mass transfer coefficient not require much imagination to assume that, thanks to the en- k [m s–1] mass transfer coefficient gineering inventiveness, one more interesting applications will L [m] module length be published in the near future. N [–] Nernst distribution number NTU [–] number of theoretical steps n [mol] molar amount Conflicts of Interest p [bar] pressure R [Jmol–1K–1] universal gas constant The authors declare no conflict of interest. T [K] Temperature V [m3] liquid volume Vz [–] distribution number Wolfgang Riedl (*1971) grad- uated in chemical engineering from Friedrich-Alexander Uni- Greek symbols versity, Erlangen-Nuremberg, in 1998 and received his docto- a, b [–] liquid phase index rate there in 2002 under Prof. d [–] density thickness Dr. A. König. He subsequently e [–] labyrinth factor worked for Kühni AG, DSM t [–] membrane porosity Nutritional Products GmbH m [–] chemical potential and LSMW GmbH (now Exyte GmbH). 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